Married man becoming Latin Rite Catholic priest if giving up sex?

The author may be invoking the Code of Canons of the African Church, which is a Patristic document from the 5th Century — actually, a 5th Century compilation of the Canons of nearly twenty synods held in ancient Africa (mostly Carthage) starting from the middle of the Fourth Century. It was held in some regard by the 1st Millennium Church, and these Canons were invoked (and in a certain sense, misinterpreted) by the Fathers of the Council in Trullo in defense of a married priesthood.

Notably:

Canon 3. Of Continence:

Aurelius the bishop said: When at the past council the matter on continency and chastity was considered, those three grades, which by a sort of bond are joined to chastity by their consecration, to wit bishops, presbyters, and deacons, so it seemed that it was becoming that the sacred rulers and priests of God as well as the Levites, or those who served at the divine sacraments, should be continent altogether, by which they would be able with singleness of heart to ask what they sought from the Lord: so that what the apostles taught and antiquity kept, that we might also keep.

Canon 4. Of the different orders that should abstain from their wives:

Faustinus, the bishop of the Potentine Church, in the province of Picenum, a legate of the Roman Church, said: It seems good that a bishop, a presbyter, and a deacon, or whoever perform the sacraments, should be keepers of modesty and should abstain from their wives.

By all the bishops it was said: It is right that all who serve the altar should keep pudicity from all women.

Canon 25. Concerning bishops and the lower orders who wait upon the most holy mysteries. It has seemed good that these abstain from their wives:

Aurelius, the bishop, said: We add, most dear brethren, moreover, since we have heard of the incontinency of certain clerics, even of readers, towards their wives, it seemed good that what had been enacted in various councils should be confirmed, to wit, that subdeacons who wait upon the holy mysteries, and deacons, and presbyters, as well as bishops according to former statutes, should contain from their wives, so that they should be as though they had them not and unless they so act, let them be removed from office. But the rest of the clergy are not to be compelled to this, unless they be of mature age. And by the whole council it was said: What your holiness has said is just, holy, and pleasing to God, and we confirm it.

Canon 38. That clerics or those who are continent shall not visit virgins or widows:

Neither clerics nor those who profess continence should enter the houses of widows or virgins without the bidding or consent of the bishops or presbyters: and then let them not go alone, but with some other of the clergy, or with those assigned by the bishop or presbyter for this purpose; not even bishops and presbyters shall go alone to women of this sort, except some of the clergy are present or some other grave Christian men.

Canon 70. What clerics should abstain from their wives:

Moreover since incontinence has been charged against some clergymen with regard to their own wives it has seemed good that bishops, presbyters, and deacons should according to the statutes already made abstain even from their own wives; and unless they do so that they should be removed from the clerical office. But the rest of the clergy shall not be forced to this but the custom of each church in this matter shall be followed.

As you can see, the same matter is repeated again and again across several canons; this makes sense if one recalls that this is a compilation of the canons of several individual councils.

At any rate, even though it shows that this practice of admitting married men to the clergy was, in the time of the Empire, tolerated, this is not the case today, as Andrew Leach correctly answered. Ecclesiastical discipline is subject to change if the Holy Father thinks it convenient.